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A Marketer of Holiday Fruit Boxes Has a New Order =2.54 cm= 2.54 \mathrm {~cm}

question 46

Essay

A marketer of holiday fruit boxes has a new order for boxes that will hold 12 pieces of
fruit. The box is to hold 4 rows of fruit, each row consisting of an orange and two
apples. In addition to the fruit there will need to be protective packing lining the
box. The mean diameter of oranges is 3.0 inches and the standard deviation is 0.25
inches. The mean diameter of apples is 4.0 inches and the standard deviation is 0.2
inches. a) If the orange diameter information had been given in centimeters rather than inches, what would be the mean and standard deviation of the orange diameter? (Note: 1 inch =2.54 cm= 2.54 \mathrm {~cm} .)
b) Suppose apples are randomly chosen for a particular row of fruit. Define random variable b=a1+a2b = a _ { 1 } + a _ { 2 } to be the space needed -- in inches -- by two randomly selected apples. What are the mean and standard deviation of bb ? c) Suppose that an additional 4 inches of box width is specified for the orange and the protective packing. Let the random variable "box width" be defined as: c=4+a1+a2c = 4 + a _ { 1 } + a _ { 2 } . How do the mean and standard deviation of bb in part (b) differ from the mean and standard deviation of the random variable, c, defined here in part (c)? Do not recalculate the mean and standard deviation.

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Definitions:

Insurable Interest

(1) In contract law, a property interest in goods being sold or leased that is sufficiently substantial to permit a party to insure against damage to the goods. (2) In the context of insurance, an interest in a person’s life or well-being that is sufficiently substantial that insuring against the person’s death or injury does not amount to a mere wagering contract.

Title

The legal right to own, use, or dispose of property or assets.

Seller

refers to an individual or entity that offers goods or services for sale to consumers or other businesses.

Merchant

An individual or business engaged in the selling of goods or services, especially those involved in wholesale or retail trade.

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